Traffic Stream Models
At the maximum flow equation 21 takes the form:
qmax=(kj/vf)(vfv0-v0 squared)=k0v0
which yields:
Equation 22
v0=vf/2
so the maximum flow is:
Equation 23
qmax=kjvf/4
It is important to remember that equation 23 holds only if a linear relationship between speed and density is assumed. This relationship was introduced by Greenshields in 1935. The linear model requires knowledge of two parameters, the free-flow speed vt1 that can be easily observed in the field (i.e., speed of traffic when flow is very low) and the jam density that is generally more difficult to estimate. An reasonable value for jam density ki results if we assume that at maximum density each vehicle occupies 25 ft of roadway space. However, field observations for the optimum density k0 generally indicate a value different that k/2